The primary thesis of our paper is that Fisher was wrong, in a fundamental way, in his belief that his theorem (“The Fundamental Theorem of Natural Selection”), implied the certainty of ongoing fitness increase. His claim was that mutations continually provide variance, and selection turns the variance into fitness increase. Central to his logic was that collectively; mutations have a net zero effect on fitness. While Fisher assumed mutations are collectively fitness-neutral, it is now known that the vast majority of mutations are deleterious. So mutations can potentially push fitness down – even in the presence of selection.

Additionally, we provided a new mathematical model for the process of mutation and selection over time, which comes in an infinite population version and a finite population version. The infinite population version uses a classical differential equations mutation/selection framework, with multiple reproducing subpopulations and mutations occurring between subpopulations, but incorporating a probabilistic distribution for mutation effects. The finite version is obtained by adding the constraint that any subpopulation with less than one organism is assumed to have no members.

Our model is backed by a literature review in Section 2 of our paper (covering 9 pages with 71 citations), with Section 2.2 discussing previous infinite populations models and Section 2.3 focusing on finite ones. Our model is new in that it includes an arbitrary distribution of mutational effects, and we do not assume mutations are 50/50 beneficial /deleterious (as did Fisher), and we did not assume that all mutations have the same fixed effect (as with Lynch’s finite population models).

Part I: Ronald A. Fisher’s Impact – First, let’s discuss Fisher and the critique by Felsenstein and Lynch of our work on Fisher’s Theorem, and its historical importance:

In their critique, JF and ML do not dispute our logic regarding Fisher’s Theorem, but provide their perspective that Fisher’s contribution to population genetics and evolutionary theory was very limited. They say,

“One of us (JF) has argued at The Skeptical Zone that they have misread the literature on population genetics. The theory of mutation and natural selection developed during the 1920s, was relatively fully developed before Fisher’s 1930 book. Fisher’s FTNS has been difficult to understand, and subsequent work has not depended on it. But that still leaves us with the issue of whether the B and S simulations show some startling behavior…”

We respectfully disagree with their perspective that Fisher’s book and Theorem had only a minor impact. The book they refer to is “Genetical Theory of Natural Selection” (GTNS), which is where he published his FTNS Theorem. To begin with, Google Scholar lists that Fisher’s book, GTNS, has been cited 20,254 times – this is not insignificant.

Below are some quotes from standard sources and leaders in the field that are consistent with our view that Fisher’s work, that his book GTNS contributed significantly to establishing the field of Population Genetics and his theorem FTNS was central to establishing Neo-Darwinian Theory.

“The Genetical Theory of Natural Selection is a point of departure in contemporaneous evolutionary thought, responsible in part for the origination of theoretical population genetics and what is commonly called the “modern synthetic theory of evolution.”

this continues,

“To be sure, Fisher’s work in statistics was revolutionary at the field’s conceptual foundation. Moreover, Fisher’s work in genetics, highlighted mainly by his 1930 The Genetical Theory of Natural Selection, would, with good company in Haldane and Wright, revolutionize biology.”

“The foundations for the critically important synthesis of Darwinism and genetics were set in the late 1920s and early 1930s by the trio of outstanding theoretical geneticists: Ronald Fisher, Sewall Wright, and J. B. S. Haldane. They applied rigorous mathematics and statistics to develop an idealized description of the evolution of biological populations. The great statistician Fisher apparently was the first to see that, far from damning Darwinism, genetics provided a natural, solid foundation for Darwinian evolution. Fisher summarized his conclusions in the seminal 1930 book The Genetical Theory of Natural Selection (Fisher, 1930), a tome second perhaps only to Darwin’s Originin its importance for evolutionary biology.5This was the beginning of a spectacular revival of Darwinism that later became known as Modern Synthesis (a term mostly used in the United States) or neo-Darwinism (in the British and European traditions).”

“In genetics, his work used mathematics to combine Mendelian genetics and natural selection; this contributed to the revival of Darwinism in the early 20th century revision of the theory of evolution known as the modern synthesis.

In 1930, The Genetical Theory of Natural Selection was first published by Clarendon Press and is dedicated to Leonard Darwin. A core work of the neo-Darwinian modern evolutionary synthesis,[29] it helped define population genetics, which Fisher founded alongside Sewall Wright and J. B. S. Haldane”

“Fisher (1918, 1922) proposed a new way of picturing populations of organisms…. Starting with this novel conception, Fisher, Haldane, and Wright developed models of the genetics of populations.”

And then,

“Moreover, this analogy allowed Fisher to vindicate Darwin’s theory of natural selection, not by empirical demonstration, but by a mathematical argument to the effect that evolution was not only possible, but also necessary” p.75.

The quotes above from Plutynski give some good perspective on Fisher’s different contributions. His 1918,1922 papers were foundational to population genetics. His 1930 GTNS book was an additional significant contribution to population genetics, and his FTNS was seen as vindicating Darwin’s theory, giving what was perceived as a rigorous argument that (Darwinian) evolution is necessary, given Mendelian genetics. The Plutynski paper is an insightful read, describing Fisher’s goals as follows:

“Fisher’s book, and the theorem in particular, is best understood as a continuation of his attempt to breach the divide between biometricians and Mendelians concerning the nature of heredity and the effectiveness of Darwinian selection. His motivation in almost all his work was to explain how it was possible to resolve this conflict, and to vindicate Darwinian selection as both a plausible and necessary cause of evolutionary change.”

“This is a book which, as a student, I weighed as of equal importance to the entire rest of my undergraduate BA course and, through the time I spent on it, I think it notched down my degree. Most chapters took me weeks, some months; … And little modified by molecular genetics, Fisher’s logic and ideas still underpin most of the ever broadening paths by which Darwinism continues its invasion of human thought. For a book that I rate only second in importance in evolution theory to Darwin’s ‘‘Origin’’ (this as joined with its supplement, ‘‘of Man’’), and also rate as undoubtedly one of the greatest books of the present century, the appearance of a variorum version is a major event. … By the time of my ultimate graduation, will I have understood all that is true in this book and will I get a First? I doubt it. In some ways some of us have overtaken Fisher; in many, however, this brilliant, daring man is still far in front.’” (Hamilton; dust-jacket of Fisher, 1930b).

“Who is the greatest biologist since Darwin? That’s far less obvious, and no doubt many good candidates will be put forward. My own nominee would be Ronald Fisher. Not only was he the most original and constructive of the architects of the neo-Darwinian synthesis. Fisher also was the father of modern statistics and experimental design. He therefore could be said to have provided researchers in biology and medicine with their most important research tools, as well as with the modern version of biology’s central theorem.”

These quotes from a variety of sources support the tenet stated in the first sentences of our paper:

“R. A. Fisher was one of the greatest scientists of the 20th century. He is considered to be the singular founder of modern statistics and simultaneously the principle founder of population genetics (followed by Haldane and Wright). Fisher was the first to establish the conceptual link between natural selection and Mendelian genetics. This paved the way for what is now called neo-Darwinian theory.” – Basener and Sanford, 2017

Central to our paper is that Fisher’s theorem, which Dawkins calls “biology’s central theorem” does not imply what Fisher thought it did (and by extension what many others thought it did). To clarify Fisher’s error, we distinguish between Fisher’s actual theorem (what he actually proved), and “Fisher’s Corollary”, which was unproven, and was really just an informal thought experiment based on his assumption that mutations have zero net effect on fitness. This corollary has clearly been falsified, which is essential to the popular concept that mutations simply supply genetic variance and natural selection converts this variance into ongoing increased fitness.

While Fisher’s Theorem is mathematically correct, his Corollary is false. The simple logical fallacy is that Fisher stated that mutations could effectively be treated as not impacting fitness, while it is now known that the vast majority of mutations are deleterious, providing a downward pressure on fitness. Our model and our correction of Fisher’s theorem (The Fundamental Theorem of Natural Selection with Mutations), take into account the tension between the upward force of selection with the downward force of mutations.

Our correction challenges a tradition central tenet of Neo-Darwinism. It is often viewed that the upward force of selection acts without consideration of the downward force of mutations. See, for example, the quote from Gould still taken as :

“The core of this synthetic theory restates the two most characteristic assertions of Darwin himself: first, that evolution is a two-stage process (random variation as raw material, natural selection as a directing force); secondly, that evolutionary change is generally slow, steady, gradual, and continuous. . . Orthodox neo-Darwinians extrapolate these even and continuous changes to the most profound structural transitions in life.” (Gould 1980)

We agree (apparently) with JF and ML that Fisher’s theorem has serious flaws. The theorem was not clearly written, and is mathematically correct but with very limited application. One of the most respected papers on Fisher’s FTNS was written by G. Price in 1972, which we quote in our paper as follows:

“Also, he [Fisher] spoke of the “rigour” of his derivation of the theorem and of “the ease of its interpretation”. But others have variously described his derivation as “recondite” (Crow and Kimura 1970), “very difficult” (Turner 1970), or “entirely obscure” (Kempthorne 1957). And no one has ever found any other way to derive the result that Fisher seems to state. Hence, many authors (not reviewed here) have maintained that the theorem holds only under very special conditions, while only a few (e.g.. Edwards 1967) have thought that Fisher may have been correct—if only we could understand what he meant! …here that this latter view is correct. Fisher’s theorem does indeed hold with the generality that he claimed for it. The mystery and the controversy result from incomprehensibility rather than error.”

At issue is that even though the flaws in Fisher’s theorem have been knowable for a long time, it has still been used as strong support for Neo-Darwinian Theory. In the quote from Gould above, mutations add raw material of variation, and selection turns variation into increase in fitness (evolutionary progress); selection is assumed to act as an upward force without considering the downward force of mutations. This is strongly linked to Fisher’s Corollary. Despite the known flaws with Fisher’s work (known at least within the population genetics community), there is still a common perception that selection acts on mutations to maximize fitness as Fisher described. As stated in the abstract of a recent 2016 paper Natural Selection and the maximization of fitness, on expansions of Fisher’s FTNS and Darwinism, by J Birch of the University of Cambridge:

“The notion that natural selection is a process of fitness maximization gets a bad press in population genetics, yet in other areas of biology the view that organisms behave as if attempting to maximize their fitness remains widespread. “

Conclusions:

R. A. Fisher was one of the three founders of population genetics, and is considered by many to be the first and primary founder. His Fundamental Theorem of Natural Selection contributed significantly to a “revival of Darwinism” (see Koonin quote above and Wikipedia). His theorem has been considered by many a significant and rigorous support for the Neo-Darwinian Theory (see quotes above).

Our paper shows that Fisher’s corollary is clearly false, and that he misunderstood the implications of his own theorem. He incorrectly believed that his theorem was a mathematical proof that showed that natural selection plus mutation will necessarily and always increase fitness. He also believed his theorem was on a par with a natural law (such as entropic dissipation and the second law of thermodynamics). Because Fisher did not understand the actual fitness distribution of new mutations, his belief in the application of his “fundamental theorem of natural selection” was fundamentally and profoundly wrong – having little correspondence to biological reality. Therefore, we have reformulated Fisher’s model and have corrected his errors, thereby have established a new theorem that better describes biological reality, and allows for the specification of those key variables that will determine whether fitness will increase or decrease.

96 thoughts on “Defending the validity and significance of the new theorem “Fundamental Theorem of Natural Selection With Mutations, Part I: Fisher’s Impact”

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You forgot to mention the the best part of the link:
“Crow and Kimura (1970) give the following example of gene substitution: “if the typical allele has a initial frequency of 10-4, a population of one million individuals will have to have nine million genetic deaths each generation if it is to substitute an average of one allele per generation.” […] Granted that most species produce numbers of progeny far in excess of those needed to have the population survive, it is difficult to understand how evolution can happen at such an enormous cost in genetic deaths. Haldane saw clearly that he was confronted by a dilemma.”

J-Mac: So, you are not doing any work? Well that just makes the two of us…but it makes you a hypocrite caught in the act…lol 😉
Nothing new, eh?

But you are free to speculate about the fitness this and fitness that and still be afraid to go out in the wild to see what the real world looks like outside of your unfounded speculations…
What do you think?

When I was a young boy, my grandfather told me a war story… In his village back in Poland, there was a Jewish family that kept it to themselves… but once a year, they would become very busy; during Christmas. One member of the family would go around the village (or more villages, I don’t know) and sell fish. The interesting thing about him was that he was deaf.. So, people bought the fish from him but they couldn’t bargain with him because he was deaf.

When Germans occupied this part of the country , the Jewish family came to my grandfather and asked for two favours:
1. They wanted a steel box to be preserved
2. They wanted my grandfather to contact their family if possible. Their name was Krauss.
The interesting thing was that the previously deaf guy did all the talking…
My grandfather told me that this trick was necessary for the Jewish family to do or they wouldn’t survive as nobody in the village wanted to do business with them because of their origins… They needed to sell the fish at the set price or they would starve to death…Therefore the deaf salesman…

One day after the war, someone showed up at my grandfathers door… According to my grandfathers’ description the man had long beard, like Joe, and a yarmulke…
He picked up the box and was about to leave when my grandfather asked what was in the box…
He said: “…you wouldn’t make a penny if you ever tried to open it….”
It turned out later that there were some genealogical family documents in the box dating back hundred of years…

Entropy: Oh crap! That changes everything! Surely nobody knew that fitness is relative to the environment. It’s not as if natural selection referred to the environment at all …. wait!

The other way around J-Mac.

It’s the population J-Mac, not the organism. The population contains lots of organisms each with variable characteristics. If the environment changes, then a subpopulation might survive the changes. If so, then the surviving individuals reproduce and their fitness-related alleles thus get fixed, and recombined, in the new population. If the environment persists, then we get mostly random genetic drift after the selection period.

Very nice idea… unfortunately a persistent one due to lack of evidence… any that is…

Agreed, but in a way that may not seem obvious. The S-coefficient can change because of the environment. In one environment it is “beneficial” and in another it is “deleterious.” In most Pop Gen, in order to make the math tractable such variability in S is removed by making it constant. There are some exceptions like this one mentioned by Joe Felsenstein in connection with my discussion (of all things, Feynman-Kac and mathematical finance):

Unless S’s variability can be described with sufficient rigor, all the math that depends on it is meaningless. So to me a lot of evolutionary theoretical genetics is like sky scrapers built on quick sand. Arlin Stolfuz echoed a different viewpoint than mine, but maybe a similar conclusion:

This is like the meaning f(x) changing over time and not being accounted for. It’s nonsense, and that’s why I’ve soured on Pop Gen. Lewontin, Wagner and Salthe, and Allen Orr have offered a similar criticism in direct and not so direct ways.

Salthe wrote that he viewed Fisher’s theorem was Neo-Darwinism theoretical cornerstone, but had some additional thoughts.

(10) The internal contradiction in its major theoretical cornerstone — Fisher’s fundamental theorem…

The negativity of the action of selection is clearly reflected in the equations of population genetics, where, in the Fisher version, the fitness of given types, m, = births minus deaths (and failures to reproduce). That is, it reflects deductions from hopeful beginnings. In the Wright-Dobzhansky version, fitness, W, = 1 minus the selection coefficient. That is, selection is represented as a deficit from maximum performance. The action that is modeled in population genetics is not variability generation, but its culling (see discussion of the Wright-Dobzhansky model in the next section for a small qualification).
A related point arises with frequent use of the phrase ‘selection for something’.

This is just an oxymoron of loose usage, as I will explain further in (9), below.
(8) its failure to explain, as Darwin hoped it would, evolutionary improvement of phenotypic characters and behaviors.
….
(10) The internal contradiction in its major theoretical cornerstone — Fisher’s fundamental theorem As mentioned above, Fisher’s theorem has it that population variance in fitness is exchanged over the generations for population fitness increase — that is, for adaptedness. A corollary would be that traits having been subjected to heavy selection pressures, because of their importance in the lives of the organisms, should be less variable than less important traits. This has been found in traits judged to be of importance for jumping in frogs (Salthe and Crump, 1977), while these same traits were not found to be significantly less variable than others in populations of frogs that walk but do not jump. Now, at the same time, note that when asked which traits are most likely to be able to evolve, evolutionary biologists, again citing Fisher’s theorem, will reply, “those that have more variability in fitness”. That is to say, traits that have been most important in the lives of organisms up to this moment will be least likely to be able to evolve further! So Fisher’s theorem is “schizoid” when one compares its postures facing the future or the past. And once again one faces the possibility of single traits evolving sequentially, building up by way of ontogenetic agency an overall adapted phenotype subjected to an increasing genetic load directed at maintenance.

J-Mac: My grandfather told me that this trick was necessary for the Jewish family to do or they wouldn’t survive as nobody in the village wanted to do business with them because of their origins… They needed to sell the fish at the set price or they would starve to death…Therefore the deaf salesman

So instead of buying fish from someone that could hear they choose to pay more than they wanted?

I can only imagine that the person involved was trying to put up enough comments up to get my earlier comment to scroll off the list of Recent Comments. Since it documented that that person had lifted material from elsewhere.

Rumraket: My days of not taking you seriously have come to a middle. Welcome back to ignore.

No! Please! No! I want to know what the ventology science is all about! Don’t leave me! I want to know why someone would believe why oceanic thermal vents have beyond human, or any other know intelligence, creative powers of life…Don’t abandon me! I care! I care! I really care!
Rum! Have mercy! You are the one…

Joe Felsenstein:
I can only imagine that the person involved was trying to put up enough comments up to get my earlier comment to scroll off the list of Recent Comments.Since it documented that that person had lifted material from elsewhere.

Joe,

Your comment was so powerful that people just wanted to appreciate it and give you due respect… That’s the side-effect of writing the top 100.000 referenced paper in the world… or something… People want a piece of you….

Hey Sal!
What do you think about environments affecting the evolution of say the Inuit and the Bushman? Both have lived for centuries in the same, steady environment…
Is that why they were so healthy comparing to the West, without any of the diseases of civilization? Was their mutation load low due to environment?
What are your thoughts, brother?

I can only imagine that the person involved was trying to put up enough comments up to get my earlier comment to scroll off the list of Recent Comments. Since it documented that that person had lifted material from elsewhere.

J-Mac,

Did your kids see you get nailed for plagiarism? It’s a good lesson for them. Be sure to point it out to them, if they haven’t noticed it already.

The last thing we’d want is for them to grow up acting like their father.

Rumraket:
Rather, insofar as fitness is declining despite selection, then at least in part, it must be because for various reasons beneficial mutations are less likely to happen than deleterious ones. And I think they generally are, but even here there is a question of proportion.

Do deleterious mutations really happen a million times more often than beneficial ones? You can certainly cherrypick literature where such ratios are suggested. On the other hand, you can also cherrypick literature that put the ratio at roughly 7:1, or 100:1. Basener and Sanford went for the million-to-one. I don’t wonder why.

Hi Rumraket,

The proportion parameter is important. The effect of this parameter on the long-term behavior is important. The JavaScript version of our model on my RIT web page allows you to modify this parameter and test:

We used 1000:1 as the ratio of deleterious to beneficial in the simulation in our paper. You can test the model at the link above, and 100:1 is around the threshold between continual decline in fitness and going to an equilibrium with mutation-selection balance. (Fraction of beneficial equal to 0.01 lives, but 0.008 goes extinct). This does not mean 100:1 is a biologically important ratio – there are a lot of the parameters that need to be examined simultaneously; we assume the magnitude of impact on fitness for deleterious and beneficial mutations is equal, while deleterious have a larger impact on average. It would also depend on population size, mutation rate, etc. etc.

Anyhow, if you want to suggest some published beneficial to deleterious ratios, I will be glad to incorporate those ratios in future evaluation of our model.

Rumraket:
Rather, insofar as fitness is declining despite selection, then at least in part, it must be because for various reasons beneficial mutations are less likely to happen than deleterious ones. And I think they generally are, but even here there is a question of proportion.

Do deleterious mutations really happen a million times more often than beneficial ones? You can certainly cherrypick literature where such ratios are suggested. On the other hand, you can also cherrypick literature that put the ratio at roughly 7:1, or 100:1. Basener and Sanford went for the million-to-one. I don’t wonder why.

Also (in addition to my previous comment on this), do you know what ratio Michael Lynch uses in his numerical simulations?

We used 1000:1 as the ratio of deleterious to beneficial in the simulation in our paper. You can test the model at the link above, and 100:1 is around the threshold between continual decline in fitness and going to an equilibrium with mutation-selection balance. (Fraction of beneficial equal to 0.01 lives, but 0.008 goes extinct). This does not mean 100:1 is a biologically important ratio – there are a lot of the parameters that need to be examined simultaneously; we assume the magnitude of impact on fitness for deleterious and beneficial mutations is equal, while deleterious have a larger impact on average. It would also depend on population size, mutation rate, etc. etc.

1000 to 1 seems like a very conservative number. In Jack Szostak experiments trying to determine the chance of a randomly generated 80 AA sequence binding to ATP he came up with a probability of 10^-11. I would logically conclude that in the application of ATP binding there is 10^11 more non functional sequences then functional ones.

In the case of your simulation you are starting with functional sequences so I think it is reasonable to assume that the chance of finding benefit is better then this but as we add mutations to this sequence it would seem that the sequence would accelerate to non function. I also think the acceleration rate would be proportional to the complexity of the function of the sequence.

A sequence that has to bind to ATP, another protein and form an enzyme function would accelerate to non function faster then a sequence that simply had to bind to ATP.

Selection and Survival are one and the same – the selected survive and the surviving have been selected. Those that disagree should show counterexample!

“Fit” as in “survival of the fittest” cannot be measured except as “survival” (circular logic). Those that disagree should show counterexample!

Natural Selection is supposed to tie both ways survivability with phenotype, but this leaves out the environment which not only affects survivability directly, but also phenotype, itself a sum of genotype plus the environment, and even genotype that is a recurrent function of previous genotypes and the environment again. So in the end, survivability is a recurrent function of genotype, an infinite continuum of environments, and other unknown factors. While survivability can be measured as can be the individual genotype, measuring a population’s genotype is daunting at best, and the impact of the ever changing environment is simply impossible to evaluate. Phenotypes are impossible to define and measure in entirety even for one individual and, in addition, phenotype changes constantly from birth to adult to old age. We do see genetic mutations (unknowable if random) and we do know that, given a similar environment, extreme genotypes reduce survivability, yet we also know that a large variety of genotypes survive just fine in any population.

I think you forgot that the neo-Darwinian fundamental belief is that natural selection is a non-random process… Due to this fundamental assumption, other assumptions must follow… increase of fitness and other evolutionary nonsense… otherwise neo-Darwiosaurs might as well go and look for another mechanism of evolution, which many have already done so…

Nonlin.org: Selection and Survival are one and the same – the selected survive and the surviving have been selected. Those that disagree should show counterexample!

“Fit” as in “survival of the fittest” cannot be measured except as “survival” (circular logic). Those that disagree should show counterexample!

Silly evolutionary biologists, paying attention to both survival and reproduction! nonlin.org has now spoken: only survival counts; whether you are able to reproduce once you survive is irrelevant.

We’ll have to go back and redo all of population genetics, I guess. Basener and Sanford will have to rewrite all their equations too because they have both birth rates and death rates in them. But nonlin.org has not pointed out that only the death rates can matter.

Joe Felsenstein: Silly evolutionary biologists, paying attention to both survival and reproduction!nonlin.orghas now spoken: only survival counts; whether you are able to reproduce once you survive is irrelevant.

We’ll have to go back and redo all of population genetics, I guess.Basener and Sanford will have to rewrite all their equations too because they have both birth rates and death rates in them.Butnonlin.orghas not pointed out that only the death rates can matter.

Wait Joe, if you are going to say that death rates equates to “survival” how can birth rates equate to selection? If these are two different concepts, does it make sense to call not ever being born to not being selected?

So every allele combination that never existed were not selected, because they never existed at all to be selected? Isn’t that nonsensical?

I think you forgot that the neo-Darwinian fundamental belief is that natural selection is a non-random process… Due to this fundamental assumption, other assumptions must follow… increase of fitness and other evolutionary nonsense… otherwise neo-Darwiosaurs might as well go and look for another mechanism of evolution, which many have already done so…

I like your “Darwiosaurs”. Will alternate that with my “Darwinistas”.

I see “natural selection” more like very bad street magic where the bus is covered with the cloth and we then are asked to imagine it disappeared without even removing the cloth and showing us the empty space.

Joe Felsenstein: Silly evolutionary biologists, paying attention to both survival and reproduction!nonlin.orghas now spoken: only survival counts; whether you are able to reproduce once you survive is irrelevant.

We’ll have to go back and redo all of population genetics, I guess.Basener and Sanford will have to rewrite all their equations too because they have both birth rates and death rates in them.Butnonlin.orghas not pointed out that only the death rates can matter.

Do you have any counterexamples? Yes or No? And don’t forget “fitness”.

But you do bring up a good point – precisely how many generations should reproduce (survive) to declare the organism has “been selected”? Look at the endangered “species”.

Wrong.
“…allowing students to track the spread of this advantageous trait over several generations. ”
…is of course survival.

Again, where’s your counterexample? In your own words, not some irrelevant link. You should start by defining your own fitness function if you can.

Perhaps you discussed. That doesn’t mean you got to anything meaningful. Let’s recap:

“Fitness is never defined independently of survivability – this renders the fitness concept redundant especially since survivability can be measured while fitness cannot. Evolutionary Fitness is defined as the quantitative representation of natural and sexual selection (reproductive success) of a genotype or phenotype in a given environment. “Survival of the fittest” is interpreted as: “Survival of the form (phenotypic or genotypic) that will leave the most copies of itself in successive generations.” Not only is survivability the only measure, but survivability also changes with the environment.”

This is not very convincing. The issue is not whether Fisher was influential, or Fisher’s 1930 book was influential, but whether FTNS is actually some sort of foundation. That is, are various key conclusions in evolutionary thinking dependent on FTNS, either directly or through other theoretical developments that depend on FTNS?

Rather than addressing that question directly, Basener and Sanford try to establish a positive answer by way of quotations. But the quotations don’t say the right things, and they are not quoting the right people. Nearly all of the quotations are about Fisher or his 1930 book or his 1920s work, without specifying FTNS. What Richard Dawkins says means nothing, because Dawkins is not in a position to judge the extent to which formal theory depends on FTNS.

The only place where Basener and Sanford cite actual theoreticians referring specifically to the FTNS, this is what they say: “Fisher’s Fundamental Theorem of natural selection is one of the most widely cited theories in evolutionary biology.”

It’s “widely cited”. The neutral theory is also one of the most widely cited theories. That does not mean it is a foundation of Darwinism.

Joe Felsenstein: Darn it, Arlin.I’m working on a reply, and you hit all the main points in only 10 sentences .

I guess we can make a clear prediction what strategy Joe Felsestein is going to apply to defend his speculations thanks to Arlin:
Fisher’s work was not as important and creationists, ID proponents and even Dawkins think it was…

We may consequently state the fundamental theorem of Natural Selection in the form : The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time.
…
Professor Eddington has recently remarked that ‘The law that entropy always increases — the second law of thermodynamics — holds, I think, the supreme position among the laws of nature’. It is not a little instructive that so similar a law [the fundamental theorem of natural selection] should hold the supreme position among the biological sciences.
…

Fisher Commenting on the FNTS
The Genetical Theory of Natural Selection
Ronald Fisher

So I consider Fisher as good as any to state what is the foundation and central part of neo-Darwinian theory. If other people disagree, that’s Ok, such are arguments how to properly attribute priority to an idea.

Is FNTS foundational to Neo-Darwinism? Depends whom you ask. I’m sure Bill and John will be happy to acknowledge other people disagree with Fisher’s assessment of the centrality of his FTNS.

PS
My favorite quote from the book:

The income derived from a Casino by its proprietor may, in one sense, be said to depend upon a succession of favourable chances

stcordova: Didn’t Fisher believe his FNTS was foundational?He’s one of the “right people” to cite isn’t he?

Not anymore….it looks like …everything was fine about Fisher’s speculations for almost 100 years. Everyone cited and would continue to cite him as long as nobody started fishing…Once Bill Basener and John Sanford caught Fisher by you know what, Darwiosaurs had no choice but to dump him…or on him…or both…

My prediction is that Fisher’s neo-Darwinian revival is going to be viewed as nothing special and it is going to die with Darwinosaurs pretending that it has always been like that but creationists and IDies read too much into the Fishery business…

stcordova: So I consider Fisher as good as any to state what is the foundation and central part of neo-Darwinian theory. If other people disagree, that’s Ok, such are arguments how to properly attribute priority to an idea.

Is FNTS foundational to Neo-Darwinism?Depends whom you ask.I’m sure Bill and John will be happy to acknowledge other people disagree with Fisher’s assessment of the centrality of his FTNS.

PS
My favorite quote from the book:

Sal,
You don’t know what you are up against… It’s not science…. If it were, Darwiosaurs would say: Wait a minute! We have this experimental evidence that proves you wrong…

They can’t do that… so they resort to other tactics that they themselves call science but they are in reality fairy tales…

They are designed to do the same thing as scientific evidence just without the scientific evidence…

They keep repeating them as often as possible because they know that if their belief is repeated often enough, people may believe it to be true…

It’s an old well proven tactic used by one of the best propaganda man ever; Joseph Goebbels:

I’m late to this party, but this appears to be making a big deal out of the obvious: as fitness approaches a local maximum, the probability of further beneficial mutations declines until an equilibrium is reached.

I’m pretty sure Fisher never intended that fitness should be infinite.